| This thesis is an attempt at mapping the fundamental many-body interactions present in interconnect structures into circuit models. Specifically, as feature sizes scale from the regime of conventional on-chip copper interconnects to that of post-silicon nanoscale interconnects (e.g. carbon nanotubes), we derive inductive coupling models that capture the dominant physical mechanisms present in each regime. For conventional copper interconnects, this amounts to deriving a hierarchical inductance model that is based on the multipole expansion of 1/r type potentials. For nanoscale interconnects on the other hand, this amounts to deriving an inductance model that is cognizant of the many-particle quantum interactions manifested in such a system. With the continuous miniaturization of feature sizes from micron scale systems to nanometer sized components, such an approach that captures the physical effects across the micro and nano regimes will become more and more important. |
